Meaning:One who is shraddhA, dhAraNA, medhA, divinity of speech and dear to the Creator BrahmA, who resides on the tip of the tongue of the devotee and gives many virtues such as self-control (peace) etc.

This describes the process of learning. How do we learn?

shraddhA. absorbing, reading to receive the knowledge.
First we must have shraddhA. The mindset to absorb, learn from the guru, book, speaker, experience, whatever that we are trying to learn from. If we don't trust the teacher to be knowledgeable, even he or she reads from a standard textbook, we will doubt. But if we believe in a palm reader, we will trust any prediction made. Children grow because they trust their parents. Every single moment is learning for them in early years. They won't survive if they didn't have the shraddhA in their parents, that whatever parents are doing is for my good.

This also means one is attentive and alert to receive.

All of a sudden many traditional practices make sense - respect for teacher and books, early morning bath (fresh and alert), sitting appropriately while studying etc.

dhAraNA
Then we must have the ability to retain what we have heard or read or experienced. This is the memory part.
Whatever we learn, must remain with us, else it is no use listening from one ear and letting go out from the other, as mothers scold their kids in India who don't listen to her sometimes. Attention and retention. This memory power can also be helped by certain foods, regular practice of being still in body and thought.

medhA
After that we must be able to process it, analyze it with our intellect. What use is it to absorb and retain if we can't process it? This too can be helped by certain foods, regular practice of being still in body and thought. But even as modern science proves, one is born with one's IQ, intellect, and there is not much that can change it.

vAk
And finally, once we have learned, solved the problem that we were having (whether to cook, build a road, find why I am on this planet, any kind of problem that caused us to sit up and search an answer by learning), once we have solved that, we must communicate it to others for their benefit as well. That is vAk. Communication. Oratory. Teaching ability. Transmitting the knowledge. The power that is knowledge.

Then the other will start a new circle of ‘absorb, retain, analye, communicate’.

And thus, learning is a cyclic process, a paramparA.

Notice how this is what a computer does as well. Input device (absorb), RAM (retain), CPU (process) and output device (communicate).

It is not that everyone has all the four abilities, actually very few
have all the four. But those who do, they shine anywhere, no matter
what field.

After a devotee (student) has followed this process thoroughly, what happens? A person who has all four abilities, and has used them appropriately, what happens to that person? Saraswati herself packs her bags and shifts her house. She builds a tiny little house on the tip of the tongue of such a devotee, student, learner. Whatever this person then speaks is truth, elegant, easily understood, and communicated. There is a very common saying in India 'Saraswati sits on his/her tongue', specially said for the great poets.

And what else happens to the student, learner?

After knowing there is so much to know, first things happens to a true student is humbleness. And then knowing how the ‘show’ works, how things interconnect, and world is interconnected, the person becomes calm. Fear comes from the unknown. Once you know, the fear is not there. You can avoid it, you can accept it, you can embrace it. After knowing the transient nature of everything, the desire quenches. One doesn’t run after this and that. One becomes self-content. If this doesn’t happen, one has not yet learned truly. The knowledge is shallow.

This lack of disturbance is called sham, the control suppression of. Of what? Of the chaos? Which chaos? The chaos of fluctuating mind-variations (chitta-vRitti). Hence a positive word like peace (shanti) has a negative word like suppress in it. Because, you natural state is peaceful and healthy (svastha). Most animals are peaceful in their own except when driven with body needs. We have created most of the un-peace due to our own mind variations, our own wanton, uncontrolled, ever multiplying desires.

When we know, we control them. We attain peace. So she is the giver of virtues like self-control and peacefulness as well.

[ There are many shlokas, aShTakamas, mantras of divinities. Many would
simply think of them as religious talk, with no other value than to the
devotee of that religious form. The beauty of most Indian forms is that
the form is there to help you, interest you, hold your attention,
inspire you. But the real value, wisdom is equally applicable to anyone.
There are two layers to everything. For a gyAna-yogI (j~nAna-yogI), one
who is only interested in knowledge and not the form, they too can
gain. But none should deny the other. That is a gyAna, karma and bhakti
are multiple ways to move forward, and most of us have all three types
of tendencies in us. ]

And now the language aspects -

yā = she who [is]

shraddhā = the mindset of, being worthy to receive the truth, ready to receive the truth